# Not micro.

This post just gathers some economic equations that I need in future posts. The following equations are straight from macroeconomics 101. Nothing special at all. The one thing that is remarkable, though, is the number of times I had to explain these equations to people that had, unlike me, been to lectures on macroeconomics. Especially here in Germany these equations seem to be unknown. I have to explain them every single time I have a discussion about economic issues with a German.

The other reason for this post is to try Latex for the first time (not really needed here but we might need higher math, like divisions,  later).

So here we go. The whole post is about this one equation:

$S - I = Ex - Im$

The difference between savings $S$ and investments $I$ equals the difference between exports $Ex$ and imports $Im$. Simple, yet important.

Let us start with the gross domestic product $Y$. It is given as the sum

$Y = C + I + G + NX$,

where

• $C$ is the consumption,
• $I$ is the investment,
• $G$ is government spending, and
• $NX$ is the difference between exports and imports.

Next we consider savings. National savings $S_{\mbox{\tiny national}}$ consist of two parts: private savings $S_{\mbox{\tiny private}}$ and government savings $S_{\mbox{\tiny government}}$:

$S_{\mbox{\tiny national}} = S_{\mbox{\tiny private}} + S_{\mbox{\tiny government}}$

The private savings $S_{\mbox{\tiny private}}$ are equal to the private disposable income minus consumption. You can either spend money or you save it. Thus

$S_{\mbox{\tiny private}} = \mbox{private disposable income} - \mbox{consumption}$,

or

$S_{\mbox{\tiny private}} = (Y - T + TR +INT) -C$,

where

• $T$ are the taxes,
• $TR$ are transfer payments from the government, and
• $INT$ are interest payments on government debt.

The government, also, can only spend or save. Here we have:

$S_{\mbox{\tiny government}} = \mbox{government income} - \mbox{government spending}$.

This gives

$S_{\mbox{\tiny government}} = (T - TR - INT) - G.$

For the national savings we then get

$S_{\mbox{\tiny national}} = S_{\mbox{\tiny private}} + S_{\mbox{\tiny government}} = Y - C - G$

Given what we know about the gross domestic product from above we obtain:

$S_{\mbox{\tiny national}} = I + NX$

This is the equation that we wanted to obtain.